The Symmetric Galerkin Boundary Element Method is employed in thin plate bending analysis in accordance with the Love–Kirchhoff kinematical assumption. The equations are obtained through the stationary conditions of the total potential energy, written for a plate whose boundary is discretized in boundary elements. Since the matrix coefficients are made up as double integrals with high order singularities, a strategy is shown to compute these coefficients in closed form. Furthermore, in order to model the kinematical discontinuities and to weight the mechanical quantities along the boundary elements, the Lagrangian quadratic shape functions, rather than C1 type (spline, Hermitian), are employed. The effectiveness of the matrix coefficients is shown through the rigid body movement technique.

Panzeca, T., Milana, V., Salerno, M. (2008). A symmetric Galerkin BEM for plate bending analysis. EUROPEAN JOURNAL OF MECHANICS. A, SOLIDS, 28(1), 62-74 [10.1016/j.euromechsol.2008.02.004].

### A symmetric Galerkin BEM for plate bending analysis

#### Abstract

The Symmetric Galerkin Boundary Element Method is employed in thin plate bending analysis in accordance with the Love–Kirchhoff kinematical assumption. The equations are obtained through the stationary conditions of the total potential energy, written for a plate whose boundary is discretized in boundary elements. Since the matrix coefficients are made up as double integrals with high order singularities, a strategy is shown to compute these coefficients in closed form. Furthermore, in order to model the kinematical discontinuities and to weight the mechanical quantities along the boundary elements, the Lagrangian quadratic shape functions, rather than C1 type (spline, Hermitian), are employed. The effectiveness of the matrix coefficients is shown through the rigid body movement technique.
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2008
Settore ICAR/08 - Scienza Delle Costruzioni
Panzeca, T., Milana, V., Salerno, M. (2008). A symmetric Galerkin BEM for plate bending analysis. EUROPEAN JOURNAL OF MECHANICS. A, SOLIDS, 28(1), 62-74 [10.1016/j.euromechsol.2008.02.004].
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